非线性弹性理论的混合能量形式广义变分原理

本文首先对弹性材料的应变能函数∑(E_ij)和余应能函数∑C(S_ij)的部分“对应”变量作Legendre变换,引进“对应”的混合余应变能函数∑_klC和混合应变能函数∑_kl。进而,给出非线性弹性理论的各种“对应”的混合能量形式广义变分原理。线性弹性理论也有相应结果,它是本文结果的特殊情况。

The Generalized Variational Principles about Blending Energy Form of Non-Linear Elasticity

First of all, this paper gives Legendre transformation for the so-called partial corresponding variables of strain energy function Σ(E_ij) and complementary strain energy function ∑C(S_ij) of the elastic materiel, and introduces the corresponding blending complementary strain energy function ∑_klC and blending strain energy function Σ_kl. Moreover, a series of generalized variational principles of the corresponding blending energy form of non-linear elasticity is given. As a special case, there exist corresponding results[1] in linear elasticity.